Liouville Theorem for Lane-Emden Equation on the Heisenberg Group
Analysis of PDEs
2024-11-01 v3
Abstract
This paper establishes some Liouville type results for solutions to the Lane Emden equation on the entire Heisenberg group, both in the stable and stable outside a compact set scenarios.Specifically, we prove that when p is smaller than the Joseph Lundgren exponent and does not equal the Sobolev exponent, 0 is the unique solution that is stable outside a compact set.
Cite
@article{arxiv.2409.00646,
title = {Liouville Theorem for Lane-Emden Equation on the Heisenberg Group},
author = {Hua Chen and Xin Liao},
journal= {arXiv preprint arXiv:2409.00646},
year = {2024}
}
Comments
There is an error in equation 2.14. For equation 2.14 to hold, the function $u$ should be cylindrical